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Zhurnal SVMO, 2018, Volume 20, Number 2, Pages 187–198 (Mi svmo700)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

The asymmetric Lorenz attractor as an example of a new pseudohyperbolic attractor of three-dimensional systems

A. O. Kazakov, A. D. Kozlov

National Research University – Higher School of Economics in Nizhny Novgorod

Abstract: In the paper a new method of constructing of three-dimensional flow systems with different chaotic attractors is presented. Using this method, an example of three-dimensional system possessing an asymmetric Lorenz attractor is obtained. Unlike the classical Lorenz attractor, the observed attractor does not have symmetry. However, the discovered asymmetric attractor, as well as classical one, belongs to a class of «true» chaotic, or, more precise, pseudohyperbolic attractors; the theory of such attractors was developed by D. Turaev and L.P. Shilnikov. Any trajectory of a pseudohyperbolic attractor has a positive Lyapunov exponent and this property holds for attractors of close systems. In this case, in contrast to hyperbolic attractors, pseudohyperbolic ones admit homoclinic tangencies, but bifurcations of such tangencies do not lead to generation of stable periodic orbits. In order to find the non-symmetric Lorenz attractor we applied the method of «saddle chart». Using diagrams of maximal Lyapunov exponent, we show that there are no stability windows in the neighborhood of the observed attractor. In addition, we verify the pseudohyperbolicity for the non-symmetric Lorenz attractor using the LMP-method developed quite recently by Gonchenko, Kazakov and Turaev.

Keywords: strange attractor, pseudohyperbolicity, homoclinic orbit, Lorenz attractor, Lyapunov exponents

DOI: https://doi.org/10.15507/2079-6900.20.201802.187-198

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UDC: 519.7

Citation: A. O. Kazakov, A. D. Kozlov, “The asymmetric Lorenz attractor as an example of a new pseudohyperbolic attractor of three-dimensional systems”, Zhurnal SVMO, 20:2 (2018), 187–198

Citation in format AMSBIB
\Bibitem{KazKoz18}
\by A.~O.~Kazakov, A.~D.~Kozlov
\paper The asymmetric Lorenz attractor as an example of a new pseudohyperbolic attractor of three-dimensional systems
\jour Zhurnal SVMO
\yr 2018
\vol 20
\issue 2
\pages 187--198
\mathnet{http://mi.mathnet.ru/svmo700}
\crossref{https://doi.org/10.15507/2079-6900.20.201802.187-198}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. O. Kazakov, E. Yu. Karatetskaya, A. D. Kozlov, K. A. Safonov, “O klassifikatsii gomoklinicheskikh attraktorov trekhmernykh potokov”, Zhurnal SVMO, 21:4 (2019), 443–459  mathnet  crossref
  • Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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